Abstract

The development of linear quantum computing within integrated circuits demands high quality semiconductor single photon sources. In particular, for a reliable single photon source it is not sufficient to have a low multi-photon component, but also to possess high efficiency. We investigate the photon statistics of the emission from a single quantum dot with a method that is able to sensitively detect the trade-off between the efficiency and the multi-photon contribution. Our measurements show, that the light emitted from the quantum dot when it is resonantly excited possess a very low multi-photon content. Additionally, we demonstrated, for the first time, the non-Gaussian nature of the quantum state emitted from a single quantum dot.

Figures (3)

Excitation level scheme and detection scheme. a) Resonant excitation coherently drives the two-photon transition between the ground |g〉 and the biexciton |b〉 state via a virtual level shown as a dashed gray line. The system decays in a cascade via the exciton |x〉 state. Of the two possible decay paths we use only the vertical polarization. Above-band excitation excites the carriers in the surrounding material. b) After spectrally resolving the emission on a diffraction grating (not shown in the figure) the spectral lines of interest (exciton and biexciton) were separated and coupled into optical fibres. A fibre beamsplitter divided the exciton light onto two detectors for state verification. The biexciton detections were used as trigger events.

The intensity autocorrelation measurement and the multi-photon contribution, p2+, plotted as a function of the single photon contribution, p1. a The exciton signal shows excellent suppression of multi-photon events which can be quantitatively expressed by intensity autocorrelation parameter of 0.031(2). The plotted data was acquired without the triggering on biexciton photon and is presented without background subtraction. The decaying peak height observable on both sides of the graph results from the blinking of the quantum dot [19]. b Here, is the set of all mixtures of Gaussian states, and the lower, white region indicates non-Gaussian states. The circles stand for results obtained in resonant and pulsed excitation while triangles for above-band and continuous wave excitation. In particular, the green circle stands for the result presented in the first row of the Table 2, and the yellow circles for the results presented in the remaining rows. The error bars represent standard deviations, the horizontal error bars of p1 are smaller than the size of the symbols. The solid blue curve represents the boundary presented in [17] and given by Eq. (4). The orange dashed line marks the limit of the detection system in continuous excitation.

Overall efficiency of the quantum dot photon source as a function of the excitation power and comparison between a single quantum dot and a down-conversion source. a) Here, the blue dashed line marks the probability of the detection of the single photon from a quantum dot under resonant excitation, p1. The gray circles show the same probability under above-band excitation. For the latter we varied the excitation power up to the saturation of the biexciton (4 mW - measured at the point where laser beam meets the cleaved edge of the sample, [15]) and observe a decrease of p1. All measurements presented in this figure were obtained using single mode fibres to collect the quantum dot emission. The coincidence window for these data was 7 ns. b) The blue dots are results of measurements performed on the emission for a down-conversion source. Here, p1 is gradually reduced through attenuation. The green dot shows the result for the quantum dot. The same point is plotted, also in green, in Fig 2(b).

Tables (3)

Table 1 Above-band excitation estimated probabilities p0, p1, p2+ and the corresponding sign of the witness, ΔW, shown for several different coincidence window widths, w. The last column also indicates the distance of the measured point to the border separating the two classes of states. This distance is given in number of standard deviations, σ

Table 2 Resonant pulsed excitation allows us to distinguish our state from a mixture of Gaussian states, which is witnessed by ΔW > 0. As in the Table 1 the last column indicates the sign of the of the witness, ΔW, (+) indicating non-Gaussian and (−) Gaussian state. The distance is also given in number of standard deviations, σ

Metrics

Table 1

Above-band excitation estimated probabilities p0, p1, p2+ and the corresponding sign of the witness, ΔW, shown for several different coincidence window widths, w. The last column also indicates the distance of the measured point to the border separating the two classes of states. This distance is given in number of standard deviations, σ

w [ns]

p0

p1 [×10−3]

p2+ [×10−8]

ΔW [σ]

1.54

0.997553(6)

2.446(6)

6.92 ± 4.89

− 1.21

2.05

0.997140(7)

2.859(7)

38.46 ± 11.59

− 3.18

2.56

0.996885(7)

3.114(7)

80.55 ± 16.78

− 4.67

3.07

0.996660(7)

3.339(7)

119.20 ± 20.40

− 5.70

3.84

0.996319(8)

3.678(8)

231.40 ± 28.50

− 8.00

Table 2

Resonant pulsed excitation allows us to distinguish our state from a mixture of Gaussian states, which is witnessed by ΔW > 0. As in the Table 1 the last column indicates the sign of the of the witness, ΔW, (+) indicating non-Gaussian and (−) Gaussian state. The distance is also given in number of standard deviations, σ

w [ns]

p0

p1 [×10−3]

p2+ [×10−8]

ΔW [σ]

10.00

0.996939(3)

3.061(3)

0.52 ± 0.52

+ 2.63

10.24

0.996938(3)

3.062(3)

1.05 ± 0.74

+ 1.16

10.75

0.996935(3)

3.064(3)

2.10 ± 1.05

− 0.17

11.24

0.996931(3)

3.067(3)

2.62 ± 1.17

− 0.60

Table 3

Photon statistics measurement was performed on a down-conversion source. The coincidence window was here equal for all the measurements w=1.2 ns

p0

p1 [×10−3]

p2+ [×10−8]

ΔW [σ]

0.8685(2)

131.4(3)

3477 ± 941

+ 146

0.95018(7)

49.81(7)

725.4 ± 123

+ 56.7

0.98081(3)

19.18(3)

100.7 ± 35.6

+ 10.1

0.99455(1)

5.45(1)

19.20 ± 8.59

− 0.98

0.997277(5)

2.723(5)

3.11 ± 2.20

− 0.80

Tables (3)

Table 1

Above-band excitation estimated probabilities p0, p1, p2+ and the corresponding sign of the witness, ΔW, shown for several different coincidence window widths, w. The last column also indicates the distance of the measured point to the border separating the two classes of states. This distance is given in number of standard deviations, σ

w [ns]

p0

p1 [×10−3]

p2+ [×10−8]

ΔW [σ]

1.54

0.997553(6)

2.446(6)

6.92 ± 4.89

− 1.21

2.05

0.997140(7)

2.859(7)

38.46 ± 11.59

− 3.18

2.56

0.996885(7)

3.114(7)

80.55 ± 16.78

− 4.67

3.07

0.996660(7)

3.339(7)

119.20 ± 20.40

− 5.70

3.84

0.996319(8)

3.678(8)

231.40 ± 28.50

− 8.00

Table 2

Resonant pulsed excitation allows us to distinguish our state from a mixture of Gaussian states, which is witnessed by ΔW > 0. As in the Table 1 the last column indicates the sign of the of the witness, ΔW, (+) indicating non-Gaussian and (−) Gaussian state. The distance is also given in number of standard deviations, σ

w [ns]

p0

p1 [×10−3]

p2+ [×10−8]

ΔW [σ]

10.00

0.996939(3)

3.061(3)

0.52 ± 0.52

+ 2.63

10.24

0.996938(3)

3.062(3)

1.05 ± 0.74

+ 1.16

10.75

0.996935(3)

3.064(3)

2.10 ± 1.05

− 0.17

11.24

0.996931(3)

3.067(3)

2.62 ± 1.17

− 0.60

Table 3

Photon statistics measurement was performed on a down-conversion source. The coincidence window was here equal for all the measurements w=1.2 ns